Journal of Convex Analysis 28 (2021), No. 3, 871--877
Copyright Heldermann Verlag 2021
Convex Bodies with Affinely Equivalent Projections and Affine Bodies of Revolution
Luis Montejano
IMATE, UNAM, Mexico
luis@im.unam.mx
We study affine bodies of revolution. This will allow us to prove that a convex body all whose orthogonal n-projections are affinely equivalent is an ellipsoid, provided n ≡ 0, 1, 2 mod 4, n > 1, with the possible exemption of n = 133. Our proof uses convex geometry and topology of compact Lie groups.
Keywords: Affinelly equivalent projections, bodies of revolution, ellipsoids.
MSC: 52A20, 52A21, 22E15.
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